Null Universal Differentiability sets

(University of Birmingham)

Abstract. Given a space X, we are looking for its subsets S as small as possible with the universal differentiability property, i.e. that every Lipschitz function on X has a point of differentiability in S.We show that every finite dimensional space contains universal differentiability sets of Minkowski dimension 1. We discuss possible generalisations and show that this result is optimal.